Here's an easy way to see what bay leaves really taste like: throw a couple in a pot of water and let it simmer. Taste it after five minutes and you'll probably get a good hit of menthol and eucalyptus (think: Vick's VapoRub). That's the chemical eugenol you're smelling, and it's the biggest constituent in the bay leaf's flavor arsenal of more than 50 compounds.
Let them simmer for longer as they would in a stew—say, an hour or so—and you'll notice that the flavor and aroma will change. The harsh nose-clearing menthol will taper down, while more complex tea-like aromas will start to come forward. Those are the flavors you're looking to add to your soups, stews, and sauces.